Question in details

Question

The weight w of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 123 pounds. Find her weight when she is 466 mi above the surface of the earth and the spacecraft is not in motion. 

Answer 1

Hi Tyler

 

From the first sentence, we have

 

w = k/d²

where w is the weight, d is the distance from the center of the earth and k is a constant.

 

We can use d = 3978 and w  = 123 to solve for k

 

123 = k/(3978)²

k = 1.946x10⁹

 

Having a value of k, we can restate the equation as

 

w = 1.946x10⁹/d²

 

Now when the astronaut is 466 miles above the surface of the earth, she is 466 + 3978 = 4444 miles from the center of the earth.

 

w = 1.946x10⁹/(4444)²

w = 98.56 pounds